On representation and querying incomplete information in databases with bags

Abstract

We extend the approach to representation of partial information based on orderings on objects from sets to multisets. We characterize orderings arising under closed- and open-world assumptions and analyze their complexity. In contrast to the set case, where orderings are first-order definable and are thus expressible in standard database query languages, the orderings on bags are not expressible in standard bag languages. We give an example of a query on nested relations whose inexpressibility in the extension of relational algebra to nested objects cannot be proved by reduction to the first-order case.